Question: Solve for $x$ and $y$ using substitution. ${-6x-6y = 12}$ ${x = 6y-9}$
Answer: Since $x$ has already been solved for, substitute $6y-9$ for $x$ in the first equation. ${-6}{(6y-9)}{- 6y = 12}$ Simplify and solve for $y$ $-36y+54 - 6y = 12$ $-42y+54 = 12$ $-42y+54{-54} = 12{-54}$ $-42y = -42$ $\dfrac{-42y}{{-42}} = \dfrac{-42}{{-42}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = 6y-9}\thinspace$ to find $x$ ${x = 6}{(1)}{ - 9}$ $x = 6 - 9$ ${x = -3}$ You can also plug ${y = 1}$ into $\thinspace {-6x-6y = 12}\thinspace$ and get the same answer for $x$ : ${-6x - 6}{(1)}{= 12}$ ${x = -3}$